Problem: Simplify the following expression and state the condition under which the simplification is valid: $y = \dfrac{k^2 + 7k - 18}{k^2 + k - 72}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{k^2 + 7k - 18}{k^2 + k - 72} = \dfrac{(k - 2)(k + 9)}{(k - 8)(k + 9)} $ Notice that the term $(k + 9)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(k + 9)$ gives: $y = \dfrac{k - 2}{k - 8}$ Since we divided by $(k + 9)$, $k \neq -9$. $y = \dfrac{k - 2}{k - 8}; \space k \neq -9$